#!/usr/bin/env python3

import sys, math
import numpy as np

def rotations(x,y,z):
    r = [
      # x is facing x
      [x, y, z],
      [x, -z, y],
      [x, -y, -z],
      [x, z, -y],
      # x is facing -x
      [-x, -y, z],
      [-x, -z, -y],
      [-x, y, -z],
      [-x, z, y],
      # x is facing y
      [-z, x, -y],
      [y, x, -z],
      [z, x, y],
      [-y, x, z],
      # x is facing -y
      [z, -x, -y],
      [y, -x, z],
      [-z, -x, y],
      [-y, -x, -z],
      # x is facing z
      [-y, -z, x],
      [z, -y, x],
      [y, z, x],
      [-z, y, x],
      # x is facing -z
      [z, y, -x],
      [-y, z, -x],
      [-z, -y, -x],
      [y, -z, -x]
    ]
    for point in r:
        yield np.array(point)

def overlap(s1,s2,off):
    se1 = set([tuple(p) for p in s1])
    se2 = set([tuple(p-off) for p in s2])
    return len(se1.intersection(se2))

def test(s1,s2):
    rot = [[r for r in rotations(*p)] for p in s2]
    rot2 = [[r[i] for r in rot] for i in range(24)]
    mc = 0
    for i in range(24):
        for p1 in s1:
            for p2 in rot2[i]:
                dif = p2 - p1
                com = overlap(s1,rot2[i],dif)    
                if com > mc:
                    mc = com
                    if mc >= 12:
                        return [r - dif for r in rot2[i]], dif
    return None, None

if __name__ == '__main__':
    nums = [[np.array([i for i in map(int,n.split(','))]) for n in line.split('\n')[1:] if n != ''] for line in open(sys.argv[1]).read().split('\n\n')]

    scanners = []
    matched = {}
    matched[0] = nums[0]
    al = set([tuple(i) for i in matched[0]])
    while len(matched) != len(nums):
        for i in range(len(nums)):
            if i in matched: continue
            r = None
            r, d = test(al,nums[i])
            scanners.append(d)
            if r != None:
                matched[i] = r
                al = al.union(set([tuple(i) for i in matched[i]]))
                break

    m = 0
    for a in scanners:
        for b in scanners:
            n = sum(abs(a[i] - b[i]) for i in range(3))
            if n > m:
                m = n

    # challenge 1
    res1 = str(len(al))
    print("challenge 1:" + "\n" +  res1 + "\n")

    # challenge 2
    res2 = str(m)
    print("challenge 2:" + "\n" +  res2 + "\n")